What is the value of the exponential expression below?
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Both runners are running at a constant speed. Say that the fastest runner goes at speed (for fast) and the slowest goes at speed
(for slow).
Let's start the observation at the moment of the passing: the two runners are in the exact same position. The laws that determine their position in the future are
This means that the difference between the two positions is given by
Now we plug in the fact that the faster speed is four more than the slower speed, i.e. . The equation for the difference becomes
And we want this difference to be 5/8 miles, so the request is
To solve for t, divide both sides by 4 to get
So, after 5/32 of a hour the two runners will be at 5/8 miles from each other.